The two-loop Sudakov form factor is computed in a $U(1)$ model with a massive gauge
boson and a $U(1)\times U(1)$ model with mass gap. We analyze the result
in the context of hard and infrared evolution equations and establish
a matching procedure which relates the theories with and without
mass gap setting the stage for the complete calculation of the dominant
two-loop corrections to electroweak processes at high energy.